Took a few days longer than I anticipated, but I got a demo site up and running:

https://demo.btct.co/

You'll have to accept the SSL certificate mismatch, as the certificate was issued for www.btct.co/btct.co.

Once you do you can create an account, it will give you 10,000.00000001 BTC, which you can then use to create assets and trade.

There are lots of little things that are broken like the LTC/BTC exchange rate quoting and a bunch of cron-based processes.  Let me know via PM if you come across any major issues. 

Cheers.